Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of λϕ4\lambda \phi^4 field theory

In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) $\phi^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field $\chi$, once the effective action is obtained by integrating over the $\phi$ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent S-D equations valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.Comment: 20 pages, 10 figure

The detection of extragalactic 15^{15}N: Consequences for nitrogen nucleosynthesis and chemical evolution

Detections of extragalactic $^{15}$N are reported from observations of the rare hydrogen cyanide isotope HC$^{15}$N toward the Large Magellanic Cloud (LMC) and the core of the (post-) starburst galaxy NGC 4945. Accounting for optical depth effects, the LMC data from the massive star-forming region N113 infer a $^{14}N/^{15}$N ratio of 111 $\pm$ 17, about twice the $^{12}C/^{13}$C value. For the LMC star-forming region N159HW and for the central region of NGC 4945, $^{14}N/^{15}$N ratios are also $\approx$ 100. The $^{14}N/^{15}$N ratios are smaller than all interstellar nitrogen isotope ratios measured in the disk and center of the Milky Way, strongly supporting the idea that $^{15}$N is predominantly of `primary' nature, with massive stars being its dominant source. Although this appears to be in contradiction with standard stellar evolution and nucleosynthesis calculations, it supports recent findings of abundant $^{15}$N production due to rotationally induced mixing of protons into the helium-burning shells of massive stars.Comment: 15 pages including one postscript figure, accepted for publication by ApJ Letter, further comments: please contact Yi-nan Chi

Quantum Kinetic Theory of BEC Lattice Gas:Boltzmann Equations from 2PI-CTP Effective Action

We continue our earlier work [Ana Maria Rey, B. L. Hu, Esteban Calzetta, Albert Roura and Charles W. Clark, Phys. Rev. A 69, 033610 (2004)] on the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. From the two-particle irreducible (2PI) closed-time-path (CTP) effective action for the Bose- Hubbard Hamiltonian, we show how to obtain the Kadanoff-Baym equations of quantum kinetic theory. Using the quasiparticle approximation, we show that the local equilibrium solutions of these equations reproduce the second- order corrections to the self-energy originally derived by Beliaev. This work paves the way for the use of effective action methods in the derivation of quantum kinetic theory of many atom systems.Comment: 21 pages, 0 figures, minor editorial changes were mad

Nuclear Bar Catalyzed Star Formation: 13^CO, C18^O and Molecular Gas Properties in the Nucleus of Maffei 2

(Abridged) We present resolution maps of CO, its isotopologues, and HCN from in the center of Maffei 2. The J=1-0 rotational lines of 12^CO, 13^CO, C18^O and HCN, and the J=2-1 lines of 13^CO and C18^O were observed with the OVRO and BIMA arrays. The 2-1/1-0 line ratios of the isotopologues constrain the bulk of the molecular gas to originate in low excitation, subthermal gas. From LVG modeling, we infer that the central GMCs have n(H_2) ~10^2.75 cm^-3 and T_k ~ 30 K. Continuum emission at 3.4 mm, 2.7 mm and 1.4 mm was mapped to determine the distribution and amount of HII regions and dust. Column densities derived from C18^O and 1.4 mm dust continuum fluxes indicate the CO conversion factor in the center of Maffei 2 is lower than Galactic by factors of ~2-4. Gas morphology and the clear ``parallelogram'' in the Position-Velocity diagram shows that molecular gas orbits within the potential of a nuclear (~220 pc) bar. The nuclear bar is distinct from the bar that governs the large scale morphology of Maffei 2. Giant molecular clouds in the nucleus are nonspherical and have large linewidths. Dense gas and star formation are concentrated at the sites of the x_1-x_2 orbit intersections of the nuclear bar, suggesting that the starburst is dynamically triggered.Comment: 50 pages, 14 figures, accepted for publication in Ap

Nonequilibrium Dynamics of Optical Lattice-Loaded BEC Atoms: Beyond HFB Approximation

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system at National Institute of Standards and Technology (NIST) where the placement of atoms in an optical lattice is controlled by using an intermediate superlattice. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: a) the Hartree-Fock-Bogoliubov (HFB) approximation, b) the next-to-leading order 1/$\mathcal{N}$ expansion of the 2PI effective action up to second order in the interaction strength and c) a second order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many body solution for a moderate number of atoms and wells. As a general feature we observe that because the second order 2PI approximations include multi-particle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution that a mean field collisionless approach fails to produce. While the second order approximations show a clear improvement over the HFB approximation our numerical result shows that they do not work so well at late times, when interaction effects are significant.Comment: 34 pages, 7 figure

Hot and Diffuse Clouds near the Galactic Center Probed by Metastable H3+

Using an absorption line from the metastable (J, K) = (3, 3) level of H3+ together with other lines of H3+ and CO observed along several sightlines, we have discovered a vast amount of high temperature (T ~ 250 K) and low density (n ~ 100 cm-3) gas with a large velocity dispersion in the Central Molecular Zone (CMZ) of the Galaxy, i.e., within 200 pc of the center. Approximately three fourths of the H3+ along the line of sight to the brightest source we observed, the Quintuplet object GCS 3-2, is inferred to be in the CMZ, with the remaining H3+ located in intervening spiral arms. About half of H3+ in the CMZ has velocities near ~ - 100 km s-1 indicating that it is associated with the 180 pc radius Expanding Molecular Ring which approximately forms outer boundary of the CMZ. The other half, with velocities of ~ - 50 km s-1 and ~ 0 km s-1, is probably closer to the center. CO is not very abundant in those clouds. Hot and diffuse gas in which the (3, 3) level is populated was not detected toward several dense clouds and diffuse clouds in the Galactic disk where large column densities of colder H3+ have been reported previously. Thus the newly discovered environment appears to be unique to the CMZ. The large observed H3+ column densities in the CMZ suggests an ionization rate much higher than in the diffuse interstellar medium in the Galactic disk. Our finding that the H3+ in the CMZ is almost entirely in diffuse clouds indicates that the reported volume filling factor (f ≥ 0.1) for n ≥ 104 cm-3 clouds in the CMZ is an overestimate by at least an order of magnitude.Comment: 33 pages, 5 figures, 3 table

Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste

Warm H2 in the Galactic center region

We present ISO observations of several H2 pure-rotational lines (from S(0) to S(5)) towards a sample of 16 molecular clouds distributed along the central ~ 500 pc of the Galaxy. We also present C18O and 13CO J=1->0 and J=2->1 observations of these sources made with the IRAM-30m telescope. With the CO data we derive H2 densities of 10e(3.5-4.0) cm-3 and H2 column densities of a few 10e22 cm-2. We have corrected the H2 data for ~ 30 magnitudes of visual extinction using a self-consistent method. In every source, we find that the H2 emission exhibits a large temperature gradient. The S(0) and S(1) lines trace temperatures (T) of ~150 K while the S(4) and S(5) lines indicate temperatures of ~ 600K. The warm H2 column density is typically ~1-2 x 10e22 cm-2, and is predominantly gas with T=150 K. This is the first direct estimate of the total column density of the warm molecular gas in the Galactic center region. These warm H2 column densities represent a fraction of ~ 30 % of the gas traced by the CO isotopes emission. The cooling by H2 in the warm component is comparable to that by CO. Comparing our H2 and CO data with available ammonia NH3 observations from literature one obtains relatively high NH3 abundances of a few 10e(-7) in both the warm and the cold gas. A single shock or Photo-Dissociation Region (PDR) cannot explain all the observed H2 lines. Alternatives for the heating mechanisms are discussed.Comment: 14 pages including figures, to be published in A&

Hamiltonian reduction of SU(2) Dirac-Yang-Mills mechanics

The SU(2) gauge invariant Dirac-Yang-Mills mechanics of spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is obtained using the gaugeless method of Hamiltonian reduction. The latter includes the Abelianization of the first class constraints, putting the second class constraints into the canonical form and performing a canonical transformation to a set of adapted coordinates such that a subset of the new canonical pairs coincides with the second class constraints and part of the new momenta is equal to the Abelian constraints. In the adapted basis the pure gauge degrees of freedom automatically drop out from the consideration after projection of the model onto the constraint shell. Apart from the elimination of these ignorable degrees of freedom a further Hamiltonian reduction is achieved due to the three dimensional group of rigid symmetry possessed by the system.Comment: 25 pages Revtex, no figure

Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model

We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional reduction predictions, obtained from conventional perturbation theory, break down below a critical dimension $d_{DR}(N)$ and we provide a description of criticality, ferromagnetic ordering and quasi-long range order in the whole $(N,d)$ plane. Below $d_{DR}(N)$, our formalism gives access to both the typical behavior of the system, controlled by zero-temperature fixed points with a nonanalytic dimensionless effective action, and to the physics of rare low-energy excitations ("droplets"), described at nonzero temperature by the rounding of the nonanalyticity in a thermal boundary layer.Comment: 20 pages, 7 figure